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A093117
a(n) = 8*a(n-1) + 21*a(n-2), with a(1)=1, a(2)=15.
3
1, 15, 141, 1443, 14505, 146343, 1475349, 14875995, 149990289, 1512318207, 15248341725, 153745416147, 1550178505401, 15630081782295, 157594402871781, 1588986940402443, 16021377983526945, 161539749616666863, 1628766934587400749, 16422470218649210115
OFFSET
1,2
FORMULA
Limit_{n -> oo} a(n+1)/a(n) converges to 4 + sqrt(37).
G.f.: x*(1+7*x)/(1-8*x-21*x^2). - Stefan Steinerberger, Nov 18 2005
a(n) = A093103(n) + 7*A093103(n-1). - G. C. Greubel, Feb 10 2023
MATHEMATICA
LinearRecurrence[{8, 21}, {1, 15}, 20] (* Harvey P. Dale, Nov 03 2020 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+7*x)/(1-8*x-21*x^2) )); // G. C. Greubel, Feb 09 2023
(SageMath)
@CachedFunction
def b(n): # b = A093103
if (n<3): return (0, 1, 8)[n]
else: return 8*b(n-1) + 21*b(n-2)
def A093117(n): return b(n) + 7*b(n-1)
[A093117(n) for n in range(1, 41)] # G. C. Greubel, Feb 09 2023
CROSSREFS
Sequence in context: A320818 A026859 A096046 * A045724 A241402 A252825
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, May 21 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 24 2004
Edited by Don Reble, Nov 04 2005
STATUS
approved